Vector Algebra Question 331
Question: Let a, b and c be vectors with magnitudes 3, 4 and 5 respectively and a + b + c = 0, then the values of a.b + b.c + c.a is
[IIT 1995; DCE 2001; AIEEE 2002; UPSEAT 2002; Kerala (Engg.) 2005]
Options:
A) 47
B) 25
C) 50
D) ? 25
Show Answer
Answer:
Correct Answer: D
Solution:
- $ \because $ $ \mathbf{a}+\mathbf{b}+\mathbf{c}=0 $ Squaring both sides, we get $ |\mathbf{a}{{|}^{2}}+|\mathbf{b}{{|}^{2}}+|\mathbf{c}{{|}^{2}}+,2(\mathbf{a},.,\mathbf{b}+\mathbf{b},.,\mathbf{c},+\mathbf{c},.,\mathbf{a})=0 $
$ \Rightarrow 2(\mathbf{a},.,\mathbf{b}+\mathbf{b},.,\mathbf{c}+\mathbf{c},.,\mathbf{a})=-,(9+16+25) $
$ \Rightarrow ,\mathbf{a},.,\mathbf{b}+\mathbf{b},.,\mathbf{c}+\mathbf{c},.,\mathbf{a}=-25. $
BETA
